Updated By SaraNextGen

On March 11, 2024, 11:35 AM

Question 1:

The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.

(Take the cost of a notebook to be Rs x and that of a pen to be Rs y.)

Answer:

Let the cost of a notebook and a pen be x and y respectively.

Cost of notebook = 2 × Cost of pen

x = 2y

x − 2y = 0

Question 2:

Express the following linear equations in the form ax + by + c = 0 and indicate the values of a, b, c in each case:

(i)   (ii)   (iii) − 2x + 3 y = 6

(iv) x = 3y (v) 2x = − 5y (vi) 3x + 2 = 0

(vii) y − 2 = 0 (viii) 5 = 2x

Answer:

(i) 

= 0

Comparing this equation with ax + by + c = 0,

a = 2, b = 3, 

(ii) 

Comparing this equation with ax + by + c = 0,

a = 1, b = , c = −10

(iii) − 2x + 3 y = 6

− 2x + 3 y − 6 = 0

Comparing this equation with ax + by + c = 0,

a = −2, b = 3, c = −6

(iv) x = 3y

1x − 3y + 0 = 0

Comparing this equation with ax + by + c = 0,

a = 1, b = −3, c = 0

(v) 2x = −5y

2x + 5y + 0 = 0

Comparing this equation with ax + by + c = 0,

a = 2, b = 5, c = 0

(vi) 3x + 2 = 0

3x + 0.y + 2 = 0

Comparing this equation with ax + by + c = 0,

a = 3, b = 0, c = 2

(vii) y − 2 = 0

0.x + 1.y − 2 = 0

Comparing this equation with ax + by + c = 0,

a = 0, b = 1, c = −2

(viii) 5 = 2x

− 2x + 0.y + 5 = 0

Comparing this equation with ax + by + c = 0,

a = −2, b = 0, c = 5